Learn

Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Higher Degree Evaluation via Root Substitution

JEE Main asked Higher Degree Evaluation via Root Substitution 2 times in 2 of the 108 shifts Lumi analysed, in 2022 and 2024. It belongs to Quadratic Roots, in Complex Numbers and Quadratic Equations (Maths). The longest wait between two years asking it was 2 years.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2022
last in 2024
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200’210.04’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20250 of 8
  • 20241 of 18
  • 20230 of 12
  • 20221 of 24
  • 20210 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: calculation.

  • Value of high-power root expression
  • Power-sum recurrence ratio

Difficulty

Easy 0Medium 2Hard 0

2 of the 2 questions had a numerical answer.

Every question

All 2 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 29 Jan 2024, Shift 1 · Q21Let α,β\alpha,\beta be the roots of the equation x2−x+2=0x^2-x+2=0 with Im(α)>Im(β)Im(\alpha)>Im(\beta). Then α6+α4+β4−5α2\alpha^6+\alpha^4+\beta^4-5\alpha^2 is…MediumNumerical value
  2. 25 Jun 2022, Shift 1 · Q26For a natural number n, let αn=19n−12n\alpha_n=19^n-12^n. Then, the value of 31α9−α1057α8\frac{31\alpha_9-\alpha_{10}}{57\alpha_8} is __________.MediumNumerical value

Shifts: 25 Jun 2022, Shift 1, 29 Jan 2024, Shift 1.

Same topic

Other ideas in Quadratic Roots

Quadratic Roots has 22 ideas JEE Main has asked; 13 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas